Abstract
The appearance of holes in crystals, developed in stressed biological structures, has motivated us to study the energy release of an initially undisturbed plate subjected to a biaxial stress state which is disturbed by a growing hole. An energy balance allows for a kinetic equation of the hole radius a. The main emphasis is placed on the calculation of the total mechanical energy-release rate by different independent concepts. Specifically, path-independent integrals represent the most convenient approach.
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References
Griffith A.A. (1921). The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A 221, 163–198
Lowenstam H.A., Weiner S. (1989). On Biomineralization. Oxford University Press, Oxford
Aizenberg J., Muller D.A., Grazul J.L., Hamann D.R. (2003). Direct fabrication of large micropatterned single crystals. Science 292, 1205–1208
Svoboda J., Gamsjäger E., Fischer F.D. (2005). Relaxation of the elastic strain energy of the misfit precipitates due to diffusion of vacancies. Philos. Mag. Lett. 85, 473–479
Svoboda J., Fischer F.D., Fratzl P., Kozeschnik E. (2004). Modelling of kinetics in multi-component multi-phase multi-particle systems I. – Theory. Mat. Sci. Eng. A 385, 166–174
Svoboda J., Turek I., Fischer F.D. (2005). Application of the thermodynamic extremal principle to modeling of thermodynamic processes in material sciences. Philos. Mag. 85, 3699–3707
Kirsch G. (1898). Die Theorie der Elastizität und die Bedürfnisse der Festigkeit. Verlag des Vereins Deutscher Ingenieure 42, 797–807
Kanninen M.F., Popelar C.H. (1985). Advanced Fracture Mechanics. Clarendon, Oxford
Anderson T.L. (1995). Fracture Mechanics: Fundamentals and Applications. CRC, Boca Raton, FL
Gdoutos E.E. (1993). Fracture Mechanics: An Introduction. Kluwer, Dordrecht
Gross D., Selig Th. (2001). Bruchmechanik mit einer Einführung in die Mikromechanik. Springer, Berlin Heidelberg New York
Inglis C.E. (1913). Stresses in a plate due to the presence of cracks and sharp corners. Trans. Naval Architects 55, 219–241
Irwin G.R. (1957). Analysis of stresses and strains near the end of a crack transversing a plate. ASME J. Appl. Mech. 24, 361–364
Rice J.R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME J. Appl. Mech. 35, 379–386
Budiansky B., Rice J.R. (1973). Conservation laws and energy-release rates. ASME J. Appl. Mech. 40, 201–203
Freund L.B. (1972). Energy flux into the tip on an extending crack in an elastic solid. J. Elast. 2, 341–349
Kienzler R., Herrmann G. (2000). Mechanics in Material Space With Applications to Defect and Fracture Mechanics. Springer, Berlin Heidelberg New York
Kienzler R., Duan Z.P. (1987). On the distribution of hoop stresses around circular holes in elastic sheets. ASME J. Appl. Mech. 54, 110–114
Márkus G. (1967). Theorie und Berechnung rotationssymmetrischer Bauwerke. Werner, Düsseldorf
Gradshteyn I.S., Ryzhik I.M. (1980). Table of Integrals, Series and Products. Academic, London
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Kienzler, R., Fischer, F.D. & Fratzl, P. On energy changes due to the formation of a circular hole in an elastic plate. Arch Appl Mech 76, 681–697 (2006). https://doi.org/10.1007/s00419-006-0048-2
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DOI: https://doi.org/10.1007/s00419-006-0048-2